If the vectors AB =-3 hat i +4 hat k and AC =5 hati-2 hatj+4 hatk are the sides of a triangle ABC, then the length of the median through A is

Question

If the vectors AB =-3 hat i +4 hat k and AC =5 hati-2 hatj+4 hatk are the sides of a triangle ABC, then the length of the median through A is (A) √14 (B) √18 (C) √29 (D) 4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7717a1f8cc34458a2d06f18766d86c96-.png" /> AD =((-3+5) hati+(0-2) hatj+(4+4) hatk/2) =(2 hati-2 hatj+8 hatk/2)= hati- hatj+4 hatk ∴ Length of median =| AD |=√18

Q. If the vectors $A B = - 3 \hat{i} + 4 \hat{k}$ and $A C = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle $A BC$ , then the length of the median through $A$ is

$14$

$18$

$29$

$4$

$A D = \frac{( - 3 + 5 ) i ^ + ( 0 - 2 ) j ^ + ( 4 + 4 ) k ^}{2}$
$= \frac{2 i ^ - 2 j ^ + 8 k ^}{2} = \hat{i} - \hat{j} + 4 \hat{k}$
$∴$ Length of median $= ∣ A D ∣ = 18$

Q. If the vectors AB=−3i^+4k^ and AC=5i^−2j^​+4k^ are the sides of a triangle ABC, then the length of the median through A is

14​

18​

29​

4

AD=2(−3+5)i^+(0−2)j^​+(4+4)k^​ =22i^−2j^​+8k^​=i^−j^​+4k^ ∴ Length of median =∣AD∣=18​

Q. If the vectors $A B = - 3 \hat{i} + 4 \hat{k}$ and $A C = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle $A BC$ , then the length of the median through $A$ is

$14$

$18$

$29$

$4$

$A D = \frac{( - 3 + 5 ) i ^ + ( 0 - 2 ) j ^ + ( 4 + 4 ) k ^}{2}$
$= \frac{2 i ^ - 2 j ^ + 8 k ^}{2} = \hat{i} - \hat{j} + 4 \hat{k}$
$∴$ Length of median $= ∣ A D ∣ = 18$